How does HNSW work??
Understanding how the HNSW algorithm works requires a closer look at its principles, its inspiration from skip lists, and how it introduces long edges to overcome traditional graph indexing challenges.
Principles of HNSW
HNSW leverages a graph structure to organize data in a way that reflects the inherent similarities between data points, forming a navigable small world network. The principle guiding this structure is to minimize the path length between any two points in the graph, ensuring that each point is reachable from any other through a small number of hops. This is achieved by organizing the data into multiple layers, with each successive layer offering a more refined view of the data.
Inspiration from skip lists
Skip lists, a data structure for storing a sorted list of items with efficient search, insertion, and deletion operations, inspire HNSW's hierarchical design. In a skip list, elements are organized into layers, with higher layers providing shortcuts for quickly traversing the list.
Similarly, HNSW constructs multiple layers of graphs, where the top layers contain fewer nodes and serve as highways for rapid navigation across the data space, directing searches closer to the target before diving into denser, lower layers for fine-grained search.
Introducing "long" edges
In the context of HNSW, "long" edges refer to connections in the upper layers of the graph that span large distances in the data space, bypassing many intermediate nodes. These edges are critical for achieving the small-world property, allowing quick jumps across the graph.
As a search query moves down from the top layer to the bottom, the length of the edges decreases, and the search area becomes increasingly localized, enabling precise identification of the nearest neighbors with minimal computational overhead.
Addressing traditional graph indexing challenges
Traditional graph indexing techniques often struggle with the curse of dimensionality, where the distance between data points becomes less meaningful in high-dimensional spaces. This makes it challenging to organize and search the data efficiently. They also suffer from poor scalability and difficulty updating the index as new data points are added or removed.
HNSW addresses these issues through its multi-layered, hierarchical approach. It allows for efficient search by reducing the dimensionality at each layer and dynamically adjusting the graph's structure without needing complete rebuilds.
This design improves search efficiency in high-dimensional spaces and supports incremental updates, making HNSW particularly well-suited for dynamic datasets where data points frequently change.
The HNSW Approach: Merits and Challenges
The HNSW indexing algorithm brings several advantages and challenges. Understanding these can help effectively leverage HNSW for vector database management and search applications.
Merits
Well documented: One of HNSW's significant advantages is its strong documentation and the wealth of research backing its methodology. This robust foundation aids developers and researchers in understanding, implementing, and optimizing the algorithm for various applications.
Preferred index in vector databases: HNSW has become the index of choice across numerous vector database engines. Its efficiency in high-dimensional vector space search operations makes it highly sought after for applications in AI, machine learning, and similar domains where rapid retrieval of information based on vector similarity is crucial.
Configurability for high recall and speed: HNSW offers exceptional configurability, allowing it to be tuned for high recall—the ability to retrieve the most relevant results—without significantly compromising search speed. This balance is particularly valuable in scenarios where the accuracy of search results is paramount, and results need to be obtained quickly.
Challenges
Memory-intensive: HNSW's performance relies heavily on storing the index entirely in memory. While beneficial for speed, this architecture choice makes HNSW more suitable for systems with substantial RAM availability. The memory requirement can become a limiting factor as the dataset grows, especially into the tens of millions of high-dimensional vectors.
Scales with memory, not disk: Unlike other data storage and indexing methods that efficiently utilize disk space, HNSW's design necessitates that the entire index fit within the available memory. This characteristic can pose challenges in scaling the system for extensive datasets or in environments where memory resources are constrained.
low efficiency when frequently updated: Frequent updates in HNSW result in inefficiency primarily because the replaced_delete(the hnswlib calls it this way) operation involves a computationally expensive process of updating neighbors. Specifically, when a node is reused, all its neighbors need to update their neighbors to reflect the changes in the graph structure. This involves traversing the graph to identify and reconnect affected nodes, which requires evaluating potential neighbors and maintaining the graph’s hierarchical structure and connectivity properties.
some points can get isolated: This issue is also caused by the replace_deleted strategy adopted by HNSW. When reusing deleted nodes, this strategy reconstructs the neighbors of the deleted node’s one-hop neighbors. During this reconstruction process, some nodes may no longer have edges pointing to them, resulting in certain nodes becoming isolated. In practical applications, this problem is generally not severe unless there are significant memory constraints or a high deletion rate.
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